A methodological study on effect size transformation in multivariate meta-analysis_Chinese Journal of Evidence-Based Medicine

Authors：

HE Xin ^1,2,3 , PAN Bei ^1,2,3 , LI Dan ¹ , MA Ning ² , LIU Qian ² , WANG Xiaoman ² , DENG Xiyuan ⁴ , LIU Xiaowei ⁵ , KONG Weize ² , LI Meixuan ² , LI Yanfei ² ,  LI Xiuxia ^1,2,3 ,  LU Yongbin ² ,  YANG Kehu ^1,2,3

1. Health Technology Assessment Center/Evidence Based Social Science Research Center, School of Public Health, Lanzhou University, Lanzhou 730000, P. R. China;
2. Evidence Based Medicine Center, School of Basic Medical Sciences, Lanzhou University, Lanzhou 730000, P. R. China;
3. Key Laboratory of Evidence Based Medicine and Knowledge Translation of Gansu Province, Lanzhou University, Lanzhou 730000, P. R. China;
4. Department of Prenatal Diagnosis Center, Gansu Provincial Maternity and Child-care Hospital, Lanzhou 730000, P. R. China;
5. The First Hospital of Lanzhou University, Lanzhou 730000, P. R. China;

Corresponding?author：

LI Xiuxia, Email: lixiuxia@lzu.edu.cn; LU Yongbin, Email: luyluyb@lzu.edu.cn; YANG Kehu, Email: yangkh-ebm@lzu.edu.cn

Keywords：

Meta-analysis; Heterogeneity; Statistical conversion; Data integration

DOI：

10.7507/1672-2531.202506169

Video：

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In meta-analysis, heterogeneity in statistical measures across primary studies can significantly affect the efficiency of data synthesis and the accuracy of result interpretation. Such inconsistencies may introduce bias in effect size estimation and increase the complexity of pooled analyses. Therefore, establishing standardized approaches for data type transformation and harmonizing different statistical measures has become a critical step in ensuring the quality of meta-analyses. To achieve efficient and scientifically rigorous data integration, researchers need to master systematic data transformation techniques and develop standardized processing strategies. Based on this need, this study provides a comprehensive summary of effect size transformation methods in meta-analysis, focusing on standardizing binary and continuous variables. It offers practical guidance to support researchers in applying these methods consistently and accurately.

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2.	楊克虎, 沙勇忠, 魏志鵬. 循證社會科學總論. 北京: 科學出版社, 2024.
3.	楊克虎, 郭麗萍. 循證教育學研究方法與實踐. 北京: 科學出版社, 2023.
4.	魏麗莉, 斯麗娟. 循證經濟學. 北京: 中國人民大學出版社, 2020.
5.	李美萱, 李艷飛, 劉謙, 等. 復現研究現狀與發展. 蘭州大學學報(醫學版), 2025, 51(3): 59-66.
6.	田金徽, 陳耀龍, 楊克虎, 等. SR/MA研究進展與挑戰. 蘭州大學學報(醫學版), 2016, 42(01): 42-47.
7.	Yao L, Sun R, Chen YL, et al. The quality of evidence in Chinese meta-analyses needs to be improved. J Clin Epidemiol, 2016, 74: 73-79.
8.	George A, Stead TS, Ganti L. What's the risk: differentiating risk ratios, odds ratios, and hazard ratios. Cureus, 2020, 12: e10047.
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13.	Chao J, Nguyen N, Po J, et al. The upper limits of risk ratios and recommendations for reporting risk ratios, odds ratios, and rate ratios. Cureus, 2023, 15(7): e37799.
14.	Sashegyi A, Ferry D. On the interpretation of the hazard ratio and communication of survival benefit. Oncologist, 2017, 22: 484-486.
15.	Shor E, Roelfs D, Vang ZM. The "Hispanic mortality paradox" revisited: meta-analysis and meta-regression of life-course differentials in Latin American and Caribbean immigrants' mortality. Soc Sci Med, 2017, 186: 20-33.
16.	Lu Y, Cen W, Wang W, et al. How big is a big hazard ratio in clinical trials. Int J Clin Trials, 2023, 10(3): 195-200.
17.	Altman DG, Bland JM. How to obtain the confidence interval from a P value. BMJ, 2011, 343: d2090.
18.	李康, 賀佳. 醫學統計學(第8版). 北京: 人民衛生出版社, 2024.
19.	Nieminen P. Application of standardized regression coefficient in meta-analysis. Bio Med Informatics, 2022, 2(3): 434-458.
20.	Gallardo-Gómez D, Richardson R, Dwan K. Standardized mean differences in meta-analysis: a tutorial. Cochrane Evid Synth Methods, 2024, 2: e12047.
21.	Peterson RA, Brown SP. On the use of beta coefficients in meta-analysis. J Appl Psychol, 2005, 90(1): 175-181.
22.	Chi KY, Li MY, Chen C, et al. Ten circumstances and solutions for finding the sample mean and standard deviation for meta-analysis. Syst Rev, 2023, 12(1): 62.
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28.	Brunner EJ, Welch CA, Shipley MJ, et al. Midlife risk factors for impaired physical and cognitive functioning at older ages: a cohort study. J Gerontol A Biol Sci Med Sci, 2017, 72(2): 237-242.
29.	Johnson W, Kuh D, Tikhonoff V, et al. Body mass index and height from infancy to adulthood and carotid intima-media thickness at 60 to 64 years in the 1946 British birth cohort study. Arterioscler Thromb Vasc Biol, 2014, 34(3): 654-660.
30.	Wang S, Luo X, Barnes D, et al. Physical activity and risk of cognitive impairment among oldest-old women. Am J Geriatr Psychiatry, 2014, 22(11): 1149-1157.
31.	孫明楠, 孫曉峰, 王海濤, 等. 老年糖尿病病人衰弱現狀及影響因素. 護理研究, 2024, 38(2): 280-286.
32.	陳耀龍, 楊克虎, 田金徽等. 循證實踐指南的制定: 國際經驗與中國實踐. 蘭州大學學報(醫學版), 2016, 42(1): 29-35.
33.	葛龍, 秦鈺, 宋忠陽, 等. 新型冠狀病毒感染恢復期常見癥中西醫結合管理循證實踐指南. 蘭州大學學報(醫學版), 2023, 49(5): 28-40,46.
34.	李艷飛, 李美萱, 魏志鵬, 等. 證據圖譜的過去、現在與未來. 蘭州大學學報(醫學版), 2025, 52(1): 1-7.
35.	楊克虎, 尚宏利, 周文杰. 循證社會科學的統計基礎. 北京: 科學出版社, 2024.
36.	楊克虎, 李秀霞. 循證衛生決策研究方法與實踐. 北京: 科學出版社, 2023.

1. 楊克虎, 許能鋒, 李曉楓. 循證醫學(第三版). 北京: 人民衛生出版社, 2019.
2. 楊克虎, 沙勇忠, 魏志鵬. 循證社會科學總論. 北京: 科學出版社, 2024.
3. 楊克虎, 郭麗萍. 循證教育學研究方法與實踐. 北京: 科學出版社, 2023.
4. 魏麗莉, 斯麗娟. 循證經濟學. 北京: 中國人民大學出版社, 2020.
5. 李美萱, 李艷飛, 劉謙, 等. 復現研究現狀與發展. 蘭州大學學報(醫學版), 2025, 51(3): 59-66.
6. 田金徽, 陳耀龍, 楊克虎, 等. SR/MA研究進展與挑戰. 蘭州大學學報(醫學版), 2016, 42(01): 42-47.
7. Yao L, Sun R, Chen YL, et al. The quality of evidence in Chinese meta-analyses needs to be improved. J Clin Epidemiol, 2016, 74: 73-79.
8. George A, Stead TS, Ganti L. What's the risk: differentiating risk ratios, odds ratios, and hazard ratios. Cureus, 2020, 12: e10047.
9. Zhang J, Yu KF. What's the relative risk. A method of correcting the odds ratio in cohort studies of common outcomes. JAMA, 1998, 280(19): 1690-1691.
10. VanderWeele TJ. On a square-root transformation of the odds ratio for a common outcome. Epidemiology, 2017, 28(6): e58-e60.
11. Knol MJ, Le Cessie S, Algra A, et al. Overestimation of risk ratios by odds ratios in trials and cohort studies: alternatives to logistic regression. CMAJ, 2012, 184(8): 895-899.
12. Higgins JPT, Li T, Deeks JJ, editors. Chapter 6: Choosing effect measures and computing estimates of effect. //In: Higgins JPT, Thomas J, Chandler J, et al. Cochrane handbook for systematic reviews of interventions version 6. 5. Cochrane collaboration, 2024.
13. Chao J, Nguyen N, Po J, et al. The upper limits of risk ratios and recommendations for reporting risk ratios, odds ratios, and rate ratios. Cureus, 2023, 15(7): e37799.
14. Sashegyi A, Ferry D. On the interpretation of the hazard ratio and communication of survival benefit. Oncologist, 2017, 22: 484-486.
15. Shor E, Roelfs D, Vang ZM. The "Hispanic mortality paradox" revisited: meta-analysis and meta-regression of life-course differentials in Latin American and Caribbean immigrants' mortality. Soc Sci Med, 2017, 186: 20-33.
16. Lu Y, Cen W, Wang W, et al. How big is a big hazard ratio in clinical trials. Int J Clin Trials, 2023, 10(3): 195-200.
17. Altman DG, Bland JM. How to obtain the confidence interval from a P value. BMJ, 2011, 343: d2090.
18. 李康, 賀佳. 醫學統計學(第8版). 北京: 人民衛生出版社, 2024.
19. Nieminen P. Application of standardized regression coefficient in meta-analysis. Bio Med Informatics, 2022, 2(3): 434-458.
20. Gallardo-Gómez D, Richardson R, Dwan K. Standardized mean differences in meta-analysis: a tutorial. Cochrane Evid Synth Methods, 2024, 2: e12047.
21. Peterson RA, Brown SP. On the use of beta coefficients in meta-analysis. J Appl Psychol, 2005, 90(1): 175-181.
22. Chi KY, Li MY, Chen C, et al. Ten circumstances and solutions for finding the sample mean and standard deviation for meta-analysis. Syst Rev, 2023, 12(1): 62.
23. Hasselblad V, Hedges LV. Meta-analysis of screening and diagnostic tests. Psychol Bull, 1995, 117: 167-178.
24. da Costa BR, Rutjes AW, Johnston BC, et al. Methods to convert continuous outcomes into odds ratios of treatment response and numbers needed to treat: meta-epidemiological study. Int J Epidemiol, 2012, 41: 1445-1459.
25. Cox DR. Analysis of binary data (2nd ed. ). Routledge, 1989.
26. 孫振球. 《醫學統計學》第4版. 北京: 人民衛生出版社, 2020.
27. Iso-Markku P, Aaltonen S, Kujala UM, et al. Physical activity and cognitive decline among older adults: a systematic review and meta-analysis. JAMA Netw Open, 2024, 7(2): e2354285.
28. Brunner EJ, Welch CA, Shipley MJ, et al. Midlife risk factors for impaired physical and cognitive functioning at older ages: a cohort study. J Gerontol A Biol Sci Med Sci, 2017, 72(2): 237-242.
29. Johnson W, Kuh D, Tikhonoff V, et al. Body mass index and height from infancy to adulthood and carotid intima-media thickness at 60 to 64 years in the 1946 British birth cohort study. Arterioscler Thromb Vasc Biol, 2014, 34(3): 654-660.
30. Wang S, Luo X, Barnes D, et al. Physical activity and risk of cognitive impairment among oldest-old women. Am J Geriatr Psychiatry, 2014, 22(11): 1149-1157.
31. 孫明楠, 孫曉峰, 王海濤, 等. 老年糖尿病病人衰弱現狀及影響因素. 護理研究, 2024, 38(2): 280-286.
32. 陳耀龍, 楊克虎, 田金徽等. 循證實踐指南的制定: 國際經驗與中國實踐. 蘭州大學學報(醫學版), 2016, 42(1): 29-35.
33. 葛龍, 秦鈺, 宋忠陽, 等. 新型冠狀病毒感染恢復期常見癥中西醫結合管理循證實踐指南. 蘭州大學學報(醫學版), 2023, 49(5): 28-40,46.
34. 李艷飛, 李美萱, 魏志鵬, 等. 證據圖譜的過去、現在與未來. 蘭州大學學報(醫學版), 2025, 52(1): 1-7.
35. 楊克虎, 尚宏利, 周文杰. 循證社會科學的統計基礎. 北京: 科學出版社, 2024.
36. 楊克虎, 李秀霞. 循證衛生決策研究方法與實踐. 北京: 科學出版社, 2023.

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